A railway half-ticket costs half the full ticket. However the reservation charge for all the tickets is constant. One full reserved ticket for a journey is Rupees 525. If the cost of one full and one half reserved ticket for the same journey is Rupees 850, then what is the reservation charge per ticket?

The correct option is Rupees 125.

Let us break down the problem step-by-step to understand how to arrive at this answer.

Step 1: Define the variables
Let the cost of a full basic ticket (excluding reservation charges) be represented by F.
Let the constant reservation charge per ticket be represented by R.

According to the problem, a half-ticket costs half of the full basic ticket. Therefore:
Cost of a half basic ticket = $\frac{F}{2}$

Step 2: Formulate the equations from the given information
The reservation charge R is constant and is added to every ticket (whether full or half).

1. The cost of one full reserved ticket is Rupees 525:
$F+R=525$ — (Equation 1)

2. The cost of one full reserved ticket and one half reserved ticket together is Rupees 850:
$(F+R)+(\frac{F}{2}+R)=850$ — (Equation 2)

Step 3: Solve the equations
Substitute the value of $F+R=525$ from Equation 1 into Equation 2:
$525+\frac{F}{2}+R=850$

Subtract 525 from both sides of the equation:
$\frac{F}{2}+R=850-525$
$\frac{F}{2}+R=325$ — (Equation 3)

Now, multiply Equation 3 by 2 to clear the fraction:
$F+2R=650$ — (Equation 4)

Next, subtract Equation 1 from Equation 4 to eliminate F:
$(F+2R)-(F+R)=650-525$
$R=125$

Thus, the reservation charge per ticket is Rupees 125.